Many systems in nature can be described in space and time. The temporal dynamics of a variable can be visualized as a 2-dimensional graph with time (t) on the abscissa and measurements of the variable (s) on the ordinate axis. This graph leaves no room for the representation of the spatial organization of the variable: that is, how values of the measurement change from place to place in the spatial domain of the system. Alternatively, measurements can be represented as a three-dimensional graph, with a set of coordinates expressing the spatial domain of the system (typically a 2-dimensional projection/reduction/representation of the original space (x, y, z)), and a luminance, intensity or color scale superimposed on this map to describe the values of the variable(s). This graph leaves no room to represent information about time; only a movie with a succession of maps would reveal how the variable changes over space and over time. Note that such a movie would not render instantaneous insight about the spatio-temporal patterning of the system because it relies on observers' memory of the previous frames, which is inherently fluctuant over time and other space; and because it depends on how/where attention is deployed during exposure to the succession of images (also fluctuant in space and in time).
In general, visualizing the fourth dimension of time using a static display (e.g., paper or an unanimated computer screen) in such a manner as to obtain a simultaneous and perceptually intuitive representation of the system is difficult due to the limits of the human perceptual system. For example, it is cumbersome to extract multi-variate information in such a manner that it can be ‘grasped’ and ‘understood’ in its complete form by human observers. In practice, massive analysis procedures are used to mine such data sets, but they never bring out the complete patterning of the system. The difficulty arises as soon as the dimensionality of the data set exceeds the dimensional constraints of the human visual system. As a result, observers of high dimensional spatio-temporal datasets are left with the burden of going back and forth between multiple partial views of the system's original variables (or its derived quantities) when working with static displays, or to employ movie animations to explore the system. However, such approaches still lack the ability to grasp all dimensions of the problem at once.
For example, the study of brain dynamics is an area which typically requires analysis of data in four dimensions. The brain is a complex system, formed by a multitude of functional units (brain areas) wired together via so-called long-range connections. At every moment, interconnected brain areas generate dynamical behaviors that must accommodate both their local (intrinsic) properties and the mutual influence they exert on each. This self-organized and non-stationary system has been shown to operate in non-equilibrium regimes. Dynamics is a chief aspect of brain function, and dynamical descriptions of the brain are irreducible to the description of time-aggregated quantities that are commonly employed to characterize this organ (topographical maps, evoked potentials, average spectra . . . ). However, conventional tools for studying brain dynamics typically provide only two- and three-dimensional representations of brain function. These representations only convey partial information about the spatio-temporal organization of the dataset and fail to integrate this information into a comprehensive, readily understandable picture.